Answer :
Let's solve the problem step by step:
1. Identify the parent function:
The given parent function is [tex]\( F(x) = \sqrt{x} \)[/tex].
2. Understand the transformation:
We need to apply a vertical stretch to the parent function. When a function is vertically stretched by a factor, each output value of the function is multiplied by that factor.
3. Apply the vertical stretch:
In this case, we are asked to vertically stretch the parent function by a factor of 7. This means that every output value of [tex]\( \sqrt{x} \)[/tex] will be multiplied by 7.
4. Formulate the new function:
To apply this transformation, we multiply the entire parent function by 7. Thus, the new function becomes:
[tex]\[ G(x) = 7 \sqrt{x} \][/tex]
5. Match the result with the provided options:
We can see that option C is:
[tex]\[ G(x) = 7 \sqrt{x} \][/tex]
Therefore, the equation of the new function after applying a vertical stretch of seven units to the square root parent function is [tex]\(\boxed{C. \, G(x) = 7 \sqrt{x}}\)[/tex].
1. Identify the parent function:
The given parent function is [tex]\( F(x) = \sqrt{x} \)[/tex].
2. Understand the transformation:
We need to apply a vertical stretch to the parent function. When a function is vertically stretched by a factor, each output value of the function is multiplied by that factor.
3. Apply the vertical stretch:
In this case, we are asked to vertically stretch the parent function by a factor of 7. This means that every output value of [tex]\( \sqrt{x} \)[/tex] will be multiplied by 7.
4. Formulate the new function:
To apply this transformation, we multiply the entire parent function by 7. Thus, the new function becomes:
[tex]\[ G(x) = 7 \sqrt{x} \][/tex]
5. Match the result with the provided options:
We can see that option C is:
[tex]\[ G(x) = 7 \sqrt{x} \][/tex]
Therefore, the equation of the new function after applying a vertical stretch of seven units to the square root parent function is [tex]\(\boxed{C. \, G(x) = 7 \sqrt{x}}\)[/tex].
